where X represents one or multiple Higgs fields. The fact that in \(\textbf {Y}_{\textbf {10}}\)  the operator \(\textbf {10}_F\textbf {10}_F\textbf {5}_H\)  is dominant implies that \(\textbf {Y}_u\)  is symmetric, i.e. \(\textbf {Y}_u=\textbf {Y}_u^T\) . In principle, also an operator \(\textbf {10}_F\textbf {10}_F\textbf {45}_H\)  would be allowed by the gauge symmetry. Such an operator would yield antisymmetric contributions to \(\textbf {Y}_u\) . However, we assume that this operator is absent (or highly suppressed) because of an appropriate family symmetry, which is consistent with the assumption of single operator dominance for the entries of \(Y_{\bar{5}}\) . Since \(\textbf {Y}_d\)  and \(\textbf {Y}_e\)  both stem from the same SU(5) operators, their entries are related via the following CG factors [1]}, [2]}:
\(\begin{split}\text{model 1 :}\hspace{56.9055pt}\textbf {Y}_e=\begin{pmatrix}0 && 1 && 0 \\\frac{3}{2} && \frac{9}{2} && 0 \\0 && 0 && \frac{3}{2}\end{pmatrix}\cdot \textbf {Y}_d^T ,\\\text{model 2 :}\hspace{56.9055pt}\textbf {Y}_e=\begin{pmatrix}\frac{4}{9} && 0 && 0 \\0 && \frac{9}{2} && 0 \\0 && 0 && \frac{3}{2}\end{pmatrix}\cdot \textbf {Y}_d^T,\end{split}\) 
